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 Izv. RAN. Ser. Mat., 2007, Volume 71, Issue 2, Pages 173–222 (Mi izv682)

Resolution of corank 1 singularities in the image of a stable smooth map to a space of higher dimension

V. D. Sedykh

Gubkin Russian State University of Oil and Gas

Abstract: We consider stable smooth maps from closed smooth manifolds to smooth manifolds of higher dimension. For maps with corank 1 singularities, we find universal linear relations between the Euler characteristics of the manifolds of singularities in their images. The calculations are based on resolving the singularities by a construction that generalizes the iteration principle from algebraic geometry.

DOI: https://doi.org/10.4213/im682

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English version:
Izvestiya: Mathematics, 2007, 71:2, 391–437

Bibliographic databases:

UDC: 515.16
MSC: 58K05, 32S20, 58K65

Citation: V. D. Sedykh, “Resolution of corank 1 singularities in the image of a stable smooth map to a space of higher dimension”, Izv. RAN. Ser. Mat., 71:2 (2007), 173–222; Izv. Math., 71:2 (2007), 391–437

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/izv682
• https://doi.org/10.4213/im682
• http://mi.mathnet.ru/eng/izv/v71/i2/p173

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. D. Sedykh, “On the Coexistence of Corank 1 Multisingularities of a Stable Smooth Mapping of Equidimensional Manifolds”, Proc. Steklov Inst. Math., 258 (2007), 194–217
2. Ohmoto T., “Singularities of Maps and Characteristic Classes”, School on Real and Complex Singularities in Sao Carlos, 2012, Advanced Studies in Pure Mathematics, 68, eds. AraujoDosSantos R., Perez V., Nishimura T., Saeki O., Math Soc Japan, 2016, 191–265
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